Solve sqrt{4/3}divsqrt{7/3}

$$\sqrt{ \frac{ 4 }{ 3 } } \div \sqrt{ \frac{ 7 }{ 3 } }$$

Evaluate

$$\frac{2\sqrt{7}}{7}\approx 0.755928946$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{4}{3}} as the division of square roots \frac{\sqrt{4}}{\sqrt{3}}.

$$\frac{\frac{\sqrt{4}}{\sqrt{3}}}{\sqrt{\frac{7}{3}}}$$

Calculate the square root of 4 and get 2.

$$\frac{\frac{2}{\sqrt{3}}}{\sqrt{\frac{7}{3}}}$$

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{\frac{7}{3}}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{2\sqrt{3}}{3}}{\sqrt{\frac{7}{3}}}$$

Rewrite the square root of the division \sqrt{\frac{7}{3}} as the division of square roots \frac{\sqrt{7}}{\sqrt{3}}.

$$\frac{\frac{2\sqrt{3}}{3}}{\frac{\sqrt{7}}{\sqrt{3}}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{2\sqrt{3}}{3}}{\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{2\sqrt{3}}{3}}{\frac{\sqrt{7}\sqrt{3}}{3}}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\frac{2\sqrt{3}}{3}}{\frac{\sqrt{21}}{3}}$$

Divide \frac{2\sqrt{3}}{3} by \frac{\sqrt{21}}{3} by multiplying \frac{2\sqrt{3}}{3} by the reciprocal of \frac{\sqrt{21}}{3}.

$$\frac{2\sqrt{3}\times 3}{3\sqrt{21}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\sqrt{3}}{\sqrt{21}}$$

Rationalize the denominator of \frac{2\sqrt{3}}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{2\sqrt{3}\sqrt{21}}{\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{2\sqrt{3}\sqrt{21}}{21}$$

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$\frac{2\sqrt{3}\sqrt{3}\sqrt{7}}{21}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{2\times 3\sqrt{7}}{21}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{7}}{21}$$

Divide 6\sqrt{7} by 21 to get \frac{2}{7}\sqrt{7}.

$$\frac{2}{7}\sqrt{7}$$